Prepared for the Keough School of Global Affairs
University of South Carolina
February 13, 2025
As the size of our data grows, we learn progressively less information.
Unless we either:
Collect all or most of the data;
Use random sampling;
Know what data we are missing.
idealstanidealstan Is a General Purpose Measurement ToolMain features:
For each person \(i\) and indicator/item \(j\),
\[ \Large \class{fragment}{\underset{\text{Data}}{Y_{ij}}} = g\left(\class{fragment}{\overset{\text{Latent Trait}}{\alpha_i}}\class{fragment}{\underset{\text{Discrimination}}{\gamma_j}} - \class{fragment}{\overset{\text{Difficulty}}{\beta_j}}\right) \]
\[ \Large \underset{\text{Data}}{Y_{ij}} = g\left(\overset{\text{Latent Trait}}{\alpha_i}\underset{\color{red}{Discrimination}}{\color{red}{\gamma_j}} - \overset{\text{Difficulty}}{\beta_j}\right) \]
To identify our latent trait, we need to use theory.
Example: if all Democrats vote for a bill and all Republicans vote against, then the bill is a positive indicator for liberal political ideology.
Encode this as \(\gamma_j > 0\).
Need at least 2 “pinned” indicators/items for bi-polar latent variables.
Greenwashing is the act of making false or misleading statements about the climate impact of a product or practice. It can be a way for companies to maintain or increase their greenhouse gas emissions. If the ad is for a political candidate, then we are not interested in whether or not it is greenwashing–only companies and affiliated entities. Is this ad engaged in greenwashing?
Bad energy policy is making life unaffordable for Canadians. Follow us to learn the truth about Canada’s oil and gas industry!
It is not possible to determine if this ad is engaged in greenwashing without more context or information about the specific claims made in the ad and whether they are accurate or misleading. The ad appears to be promoting the oil and gas industry, which could potentially involve making claims that are intended to downplay the environmental impact of the industry or overstate its benefits, but this does not necessarily mean that the ad is engaging in greenwashing. Without more information, it is not possible to make a definitive determination about whether the ad is greenwashing or not.
Greenwashing is the act of making false or misleading statements about the climate impact of a product or practice. It can be a way for companies to maintain or increase their greenhouse gas emissions. If the ad is for a political candidate, then we are not interested in whether or not it is greenwashing–only companies and affiliated entities. Is this ad engaged in greenwashing?
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yes, the ad is engaging in greenwashing by using a reference to the Second Amendment (which primarily deals with gun rights) and suggesting that wearing their jersey supports it, while also using patriotic imagery and language, without any clear connection to climate change or sustainability. The use of the phrase “End of Winter SALE” and the offer of a discount on the entire order further suggests that this is not primarily an environmental message, but rather a marketing ploy to increase sales.
We can make use of big data, but we also need big models.
Sometimes new wine works best in old wineskins.
Future research: integration with causal inference, more dimensions, multi-level latent variables.
https://chi-feng.github.io/mcmc-demo/app.html?algorithm=HamiltonianMC&target=banana
For a given item \(j\) and person \(i\),
\[\begin{align} \alpha_i &\sim \text{Normal}(0,3)\\ \gamma_j &\sim \text{GeneralizedBeta}(2,2)\\ \beta_j &\sim \text{Normal}(0,3) \end{align}\label{eq-genprior}\]
For an item \(j\), person \(i\), and missingness indicator \(r\),
\[ \prod^{I}_{i=1} \prod^{J}_{j=1} \begin{cases} \zeta(\alpha_{i}'\nu_j - \omega_j ) & \text{if } r=0, \text{ and} \\ (1-\zeta({\alpha_{i}'\nu_j - \omega_j}))L(Y_{ijr}|\alpha_i,\gamma_j,\beta_j) & \text{if } r=1 \end{cases} \qquad(1)\]
For a given person \(i\) and time point \(t\),
\[ \alpha_{it} \sim N(\delta_i+ \alpha_{it-1},\sigma_i) \qquad(2)\]
For a given person \(i\) and time point \(t\),
\[ \alpha_{it} = \delta_i + \psi_i\alpha_{it-1} + \sigma_i\epsilon_{it} \qquad(3)\]
For a given person \(i\) and time point \(t\),
\[ f(x_t) \sim N(\mu(f(x_t)),\Sigma(f(x_t))) \qquad(4)\]
For a given person \(i\) and time point \(t\),
\[ S_{q,d}(t) = B_{s,d}(t)A_i \qquad(5)\]
For each item \(j\), person \(i\), and external covariate ,
\[ \frac{\partial Y_{ijtm}}{\partial x} \left( L_m(\gamma_j(\alpha_{it} + \phi x) - \beta_j) \right) = \phi \gamma_j L_m'(\gamma_j(\alpha_{it} + \phi x) - \beta_j) \qquad(6)\]